K2 Targets Observed with SPHERE/VLT: An M4-7 Dwarf Companion Resolved around EPIC 206011496^{* †}

After the discovery of thousands of exoplanets, mainly thanks to the transit and radial velocity (RV) methods, we have moved from an era of detection into an era of characterization of exoplanets. But to properly characterize a planet, one needs a measurement of its radius and mass. While the Kepler (Borucki et al. 2010) mission provided a large amount of exoplanets, the extended mission K2 (Howell et al. 2014) targets brighter stars, and represents the first opportunity to massively characterize both the mass and radius of Earth-sized to Neptune-sized exoplanets.

In this context, the role of high-resolution imaging (HRI) is dual. First, HRI helps confirm the planetary nature of the detected transit. Second, it allows us to significantly reduce the possible bias of the measurement of the planetary radius (e.g., Léger et al. 2009; Ciardi et al. 2015).

Concerning the first role, HRI is not intended to directly confirm the nature of the transit. Confirmation is achieved through the detection of the planetary signature with another, independent observation technique (typically RV). However, when independent observations cannot constrain the planetary nature of the transits, one can perform a probabilistic validation of the transit nature (e.g., Díaz et al. 2014; Moutou et al. 2014; Santerne et al. 2015). This consists of comparing the posterior probability of all the possible scenarios for the presence of the transit given all available data. In this context, the presence of nearby contaminant stars should be closely investigated, and in the case of very shallow transits, special attention should be given to the very close vicinity of the target. Hence, HRI helps answer the following question: is there a chance-aligned eclipsing system in the angular vicinity of the target that could mimic the transit detected in the target's light curve? Given that the transit of an Earth-sized to Neptune-sized planet can be mimicked by a background eclipsing system down to 10 and 7.5 mag fainter than the target star, respectively (see the detailed calculation in Appendix A), we need HRI instruments capable of reaching such contrasts within ≈6'', the typical diameter of Kepler's broad point-spread function (PSF). More specifically, HRI helps with identifying very close contaminants missed by classical imaging.

Concerning the second role of HRI, assuming that we can confirm the planetary nature of the transit, and according to Equation (1), the presence of a contaminant would still bias the measurement of the transit depth (TD) and thus the measurement of the planetary radius. Ciardi et al. (2015) showed that ignoring the contamination can lead to an underestimation of planetary radii up to a factor 1.5, corresponding to an overestimation of the planet bulk density of a factor ∼3, for the Kepler Objects of Interest. However, they claimed that with additional HRI, the bias in the planetary radii underestimation drops to 1.2.

We present observations of six K2 targets performed with the VLT/SPHERE instrument from 2016 to 2017. With its capacity to detect companions of Δmag below 12 down to separations of 01 around stars brighter than 11 mag in the R band, SPHERE (Beuzit et al. 2008) is one of the few instruments capable of detecting contaminants faint enough to mimic an Earth-sized to Neptune-sized transit within Kepler's PSF. In Section 2 we present the sample of our K2 targets and explain the observing modes and data reduction processes in Section 3. Section 4 describes the results of our observations, which are discussed in Section 5.

Our sample comprises K2 targets from campaigns #1 to #8. We selected stars whose light curve exhibits a transit-like signal of depth below 100 ppm, compatible with the transit of an Earth-sized or Neptune-sized planet (see Appendix A). To reach the sensitivity required to detect the corresponding contaminants (see Section 1 and Appendix A), we had to restrict ourselves to stars brighter than the 13th magnitude in the Kepler bandpass.

K2 targets presenting transit-like events were identified using both the already published lists of transiting planetary candidates (see Table 3 in Appendix B for references) and detections made by our team. For the latter, we first used the POLAR software (Barros et al. 2016) to reduce the target-pixel files and produce high-precision light curves. These were then searched for transit-like events with two independent analyses, as described in Barros et al. (2016) and Armstrong et al. (2015). During these searches, we checked the detected transit events against a set of diagnostics that allowed us to identify false-positives: even/odd TD differences, out-of-transit variations, and the presence of a secondary eclipse.

We obtained a sample of 6 stars harboring the most promising Earth-sized and Neptune-sized planetary candidates whose natures were not confirmed at the time. These targets are listed in Table 3 (Appendix B) along with the most important information regarding the transits detected in their light curves, the corresponding size of the exoplanetary candidate, and current literature (Appendix B).

The SPHERE observations of our K2 targets were performed during the ESO periods P98 and P99 through the open time programs 98.C-0779(A) and 99.C-0.276(A). The data were acquired using the IRDIFS mode, in the pupil-tracking mode with the N_ALC_YJH_S coronagraph (185 mas diameter). IRDIS (InfraRed Dual-band Imager and Spectrograph, Dohlen et al. 2008) was used in the dual-band imaging mode (DBI, Vigan et al. 2010) in the H2H3 filters (λ_H2 = 1.587 μm, λ_H3 = 1.667 μm) and IFS (Integral Field Spectrograph; Claudi et al. 2008) in the YJ bands (0.95–1.35 μm, R = 50). A description of the observations is provided in Table 4 (Appendix C).

The data were reduced at the SPHERE Data Center (DC; Delorme et al. 2017) using the SPHERE Data Reduction and Handling software (DRH; Pavlov et al. 2008). Bad-pixel and dark-field corrections were applied during the data treatment, as well as a frame selection using the routine offered by the DC for all targets except EPIC 206011496. Frames for which the flux in the central spot are beyond 1σ from the median flux are rejected, which allows us to keep most good images. In general, ∼1/3 of the frames were removed after selection. Concerning EPIC 206011496, we detected a companion at the edge of the IFS field of view of epoch 2017 August 14 (see Section 4.2). The companion was within the IFS field of view for only 9 frames. These were used in the analysis. We selected the bad frames in the IRDIS data using the method described in Ligi et al. (2018) for the LAM-ADI pipeline, i.e., we excluded frames presenting a flux above or below 1.5σ of the mean flux calculated from the moving-average of the 100 frames around the considered one. We then used the Specal routine (Galicher et al. 2018) to apply different data reduction algorithms, namely the TLOCI (Template-Locally Optimized Combination of Images; Marois et al. 2014), PCA (Principal Component Analysis; Soummer et al. 2012), cADI (Classical Angular Differential Imaging; Marois et al. 2006), and noADI. The different algorithms differ in how they discriminate planets from speckle patterns (Delorme et al. 2017), i.e., in their description of stellar speckles, which are then subtracted to the image. In all the algorithms that we used (except noADI) the images were then rotated to a common orientation, averaged, and mean-combined. Using these different algorithms allows us to verify that hypothetical artifacts are not interpreted as planetary candidates, or inversely, that no candidate is missed. To confirm the results, the data of EPIC 206011496 of epoch 2017 August 14 were also reduced with the LAM-ADI (Vigan et al. 2015) and the ASDI-PCA (Mesa et al. 2015) pipelines. The results are similar to those obtained with the SPHERE DRH.

4.1. No Detection around EPIC 220383386, EPIC 206157908, EPIC 206144956, EPIC 205904628, and EPIC 206247743

Figure 1 shows the IFS images of all six targets (IRDIS images can be found in Figure 5 in Appendix D). We do not detect any candidate companion or any background star around five stars, but we detect a bright candidate around EPIC 206011496 (see Section 4.2). We calculated the detection limits for all five stars using the Specal routine (Galicher et al. 2018) offered by the SPHERE DC. Objects with contrasts between ∼12.5 and 13.5 mag and separations between 02 and 6'' in IRDIS data should have been detected (Figure 2, top). In IFS data, for the same separation of 02, the detection limit is in the range of ∼8.5–12.5 mag.

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The detection limits are below the magnitudes of background eclipsing binaries that could mimic Earth-sized to Neptune-sized transits (in the case of a false-positive scenario). This means that our SPHERE observations entirely eliminate the possibility of such scenarios in the FoV covered by SPHERE, which drastically decreases the likelihood of false-positive scenarios, since the FoV covered by SPHERE is very large. Background binary or tertiary systems that cannot be detected with our observations because they are too faint could not have caused the transits by themselves. Had we detected background multiple systems, spending time on RV vetting on these K2 candidates would have been useless. Only eclipsing binaries hidden behind the coronagraph cannot be detected, but this is very unlikely because the area covered by the coronagraph is tiny (∼36 times smaller than the FoV). Our observations therefore significantly increase the chance that the detected transits are caused by real exoplanets, and encourage RV vetting to confirm them.

4.2. Detection of an M Dwarf around EPIC 206011496

We detect a bright companion (EPIC 206011496 B) close to EPIC 206011496, both in IRDIS and IFS data for epoch 2017 August 14 (Figures 1 and 5 in Appendix D) and in IRDIS data only for the two other epochs (Table 4, Appendix C). We reach a median signal-to-noise (S/N) ratio of 66.5 in IFS (YJ band) and average S/N of 84.6 in IRDIS (H band) for this companion, for epoch 2017 August 14 (PCA reduction). We thus performed an astrometric and spectroscopic analysis of the companion in the following sections.

4.2.1. Proper Motion

We computed the position of the companion relative to the primary star between the data sets, using the parallax of the primary star and its proper motion (see Table 1), along with SPHERE astrometry from the three observing periods. We also added the position of the companion found with the NIRC2/Keck instrument (see Appendix B). The predicted positions of a hypothetical background object at the four observing periods are represented by empty symbols, while the measured positions are shown with plain symbols on Figure 3. It is clear that the relative motion between the primary and the companion is insignificant. The companion is thus linked to the primary star and corresponds to the one detected with NIRC2/Keck in 2015.

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Table 1.  Parameters of EPIC 206011496

Parameter	Value	References
R.A. [hh mm ss]	22 48 07.5629	Gaia DR1 (1)
Decl. [deg mm ss]	−14 29 40.837	Gaia DR1 (1)
Parallax [mas]	7.183 ± 0.051	Gaia DR2 (2)
μα [mas yr−1]	30.935 ± 1.521	Gaia DR1 (1)
μδ [mas yr−1]	−23.702 ± 0.971	Gaia DR1 (1)
J [mag]	9.726 ± 0.026	2MASS catalog (3)
H [mag]	9.312 ± 0.022	2MASS catalog (3)
K [mag]	9.259 ± 0.027	2MASS catalog (3)
Fbol [erg cm−2 s−1]	1.067 ± 0.0023 · 10−9	VOSA (4)
Teff [K]	5400 ± 50	VOSA (4)
L [L⊙]	0.646 ± 0.011	VOSA (4)
[M/H]	0.0	VOSA (4)
R [R⊙]	0.92 ± 0.02	This work
Age (old) [Gyr]	${2.42}_{-1.47}^{+3.76}$	This work
Mass (old) [M⊙]	0.974 ± 0.044	This work
Age (young) [Myr]	${77.91}_{-0.46}^{+1.11}$	This work
Mass (young) [M⊙]	0.995 ± 0.056	This work

References. (1) Gaia Collaboration (2016), (2) Gaia Collaboration et al. (2018), (3) Cutri et al. (2003), (4) Bayo et al. (2008).

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4.2.2. Determination of EPIC 206011496 A Parameters

The parameters of EPIC 206011496 B depend on the age of the system. We estimated the bolometric flux and the luminosity of the primary star using several photometric catalogs given by the VOSA tool (Bayo et al. 2008).¹⁰ In the case of EPIC 206011496, we kept all photometric data points but the VISTA data, because they were flagged as bad data. We used the upper limit of the WISE.W4 data. The derived bolometric flux and associated luminosity are given in Table 1, and were obtained by combining the BT-NextGen AGSS2009 model (Allard et al. 2011) and the Gaia DR2 parallax. The best-fit model corresponds to an effective temperature of T_eff = 5400 ± 50 K, which is in very good agreement with the Gaia DR2 temperature (${5390}_{-33}^{+194}\,{\rm{K}}$) and within the error bars given by the model. However, it is lower than the previous determination of 5509 ± 50 K by Vanderburg et al. (2016b). Their estimation was based on photometry and on the Hipparcos distance (231 pc), which places EPIC 206011496 much further away than Gaia (${139.22}_{-0.97}^{+0.98}\,\mathrm{pc}$). They find a metallicity (0.07 ± 0.08 dex) compatible with ours, but both values are lower than the one derived by Huber et al. (2016). Using our derived T_eff and luminosity, we calculated the stellar radius to be R = 0.92 ± 0.02 R_⊙ using a standard propagation of errors. This value is much smaller than that of 1.714 ± 1.278 R_⊙ derived by Huber et al. (2016), who also used Hipparcos distance.

Finally, we used the PARSEC models (Bressan et al. 2012) to derive the age and mass of the star. We used the technique described in Ligi et al. (2016) to interpolate the isochrones and compute the errors. As often, we obtained two different solutions: an old age of ${2.42}_{-1.47}^{+3.76}\times {10}^{9}$ years with a 57% probability corresponding to a mass of 0.974 ± 0.044 M_⊙, and a younger age of ${77.91}_{-0.46}^{+1.11}\times {10}^{6}$ years (43% prob.) with a mass of 0.995 ± 0.056 M_⊙ (Table 1). With no additional information on the star, we cannot choose between these two ages. Considering the derived probability and the lack of infrared excess in the spectral energy distribution (SED), we adopted the solution that corresponds to an evolved star of ${2.42}_{-1.47}^{+3.76}\,\mathrm{Gyr}$.

4.2.3. Spectral Analysis of EPIC 206011496 B

Using both the IFS and IRDIS photometric values, we obtained a low-resolution (R = 50) spectrum of EPIC 206011496 B in contrast. To convert it into flux, we first use a flux-calibrated BT-NEXTGEN (Allard et al. 2012) synthetic spectrum of EPIC 206011496 A, assuming T_eff = 5400 K, $\mathrm{log}(g)=2.5$, and [M/H] = 0.0 dex, which gives the best fit with the SED of EPIC 206011496 A. We then multiply the flux in contrast by the synthetic spectrum of EPIC 206011496 A. The synthetic spectrum was also retrieved through the VOSA tool. Since the system is probably old (see Section 4.2.2), we made the fit to a library of M template spectra taken from the library of Cushing et al. (2005) and Rayner et al. (2009). The best fit is obtained for the M4 spectral type star HD 214665 (see Figure 4, top, with χ² = 0.454). We also tested the fitting with sample spectra of field dwarfs from the Spex Prism spectral Libraries (Burgasser 2014),¹¹ resulting in a best fit corresponding to the M7 star CTI021845.9+280047. With a fit done using the MLT field dwarfs from the IRTF library, we find a worse fit (χ² = 1.738, GJ406 spectrum, M6 dwarf). As a result of this analysis, we adopt for EPIC 206011496 B a spectral type of M4-7.

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4.2.4. Astrometry and Photometry

The spectrum of the companion is also supported by its position in the color–magnitude diagram (CMD) built with field objects from the Spex Prism spectral Libraries (Burgasser 2014) and from Leggett et al. (2000). A detailed description of how the CMD is built can be found in Bonnefoy et al. (2018). In our analysis, the Gaia DR2 parallaxes have been added for M and L field dwarfs. From the H and J photometry of the primary star, its distance, and the contrast of the companion, we computed its absolute magnitude in the H and J bands. In Figure 4 (bottom), EPIC 206011496 B is compared to field objects, and its position suggests an M0-M5 spectral type.

We computed the detection limit of the 2017 August 14 and 2017 September 15 observations of EPIC 206011496 from IRDIS data in magnitude using the method described in Galicher et al. (2018). Then, we used the COND 2003 model (Baraffe et al. 2003) to convert the detection limits in mass, which depends on the age of the system, the distance, and the magnitude (Figure 2). We only consider the old age. Using the COND model, we also derived the mass of the companion for each spectral band (Table 2) using the method described in Bonavita et al. (2017). We considered the median contrast in the wavelength range between 0.95 and 1.15 μm for the Y band, and that between 1.15 and 1.35 μm for the J band. We also estimated the companion separation and position angle for each band, with the uncertainties taking into account all the possible sources of errors. We finally derive a median mass of 0.38 ± 0.06 M_⊙ at a separation of 977.12 ± 0.73 mas for EPIC 206011496 B from the data of epoch 2017 August 14. This mass estimation is compatible with the spectral type of M4-7, and is well above the detection limit in all our data.

Table 2.  Astrometry and Photometry of EPIC 206011496 B

Filter	ΔMag	Mass	Sep		PA
		(M⊙)	(mas)	(au)	(°)
H2	3.19 ± 0.06	0.39 ± 0.03	976.15 ± 0.86	140.05 ± 0.12	247.85 ± 0.04
H3	3.13 ± 0.06	0.38 ± 0.03	976.75 ± 0.97	140.13 ± 0.14	247.87 ± 0.04
Y	4.39 ± 0.02	0.30 ± 0.03	977.90 ± 0.27	140.30 ± 0.04	248.81 ± 0.01
J	4.11 ± 0.02	0.27 ± 0.02	977.12 ± 0.28	140.19 ± 0.04	248.82 ± 0.01
Adopted Values (Medians and Standard Deviations)
	4.11 ± 0.64	0.38 ± 0.06	977.12 ± 0.73	140.19 ± 0.11	248.81 ± 0.55

Note. The contrast values in the J2 and J3 bands are 3.97 ± 0.05 and 3.81 ± 0.05, respectively.

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We observed with SPHERE/VLT six K2 targets that show transit light curves compatible with Earth-sized to Neptune-sized exoplanets. For EPIC 205904628, EPIC 206144956, EPIC 206157908, EPIC 206247743, and EPIC 220383386 we do not detect any object in their close environments or in their backgrounds. With deep detection limits down to ∼10 to 14 mag into Kepler's PSF, the probability of such configurations as chanced-aligned eclipsing systems causing a TD in the light curves, is tremendously decreased.

We detect a companion around EPIC 206011496 at a wide separation of 140.19 ± 0.11 au. Its spectrum is compatible with an M4-7 star and the proper motion analysis shows that it is bounded to the primary star. Given its separation, its orbital period (close to 7000 years) cannot cause the observed transit. Using COND evolutionary models, we estimate its mass to be 0.38 ± 0.06 M_⊙. Our SPHERE/VLT data are used to confirm, with Keck/NIRCS2 data, an exoplanetary candidate, which is presented in Lam et al. (2018).

Using only our observations, we cannot unambiguously conclude whether the observed transit occurs on EPIC 206011496 A or on EPIC 206011496 B. To compute the approximate transiting exoplanet radius, we consider the radius range (0.26–0.12 R_⊙) and temperature range (3100–2500 K) for M4–M7 dwarfs given by Kaltenegger & Traub (2009), and the average wavelength of the K2 bandpass (660 nm). We then calculate the luminosity ratio of both stars at this wavelength using Planck's law. Assuming that the transit occurs on EPIC 206011496 A and given the TD (Table 3, Appendix B), the exoplanet would have a radius of ∼1.59–1.62 R_⊕ considering the stellar radius in Table 1 and the contamination by EPIC 206011496 B. Here, the contamination by the companion is negligible as expected and the transiting planets remains in the super-Earth regime. If the exoplanet transited EPIC 206011496 B, and taking the companion's radius between 0.12 and 0.26 R_⊙, the exoplanet radius would be included between ∼2.17 and 2.39 R_⊕. In this case, the exoplanets would fall into the mini-Neptune regime. In their paper, Lam et al. (2018) confirm that the planet transits the primary star.

As highlighted by Matson et al. (2018) and Kraus et al. (2016), the impact of a stellar companion on planetary formation still remains an open question. Our SPHERE observations reveal a companion star in an exoplanetary system and thus contribute to the study of formation mechanisms, architecture, and binarity in exoplanetary systems, and could be integrated into larger imaging surveys (like e.g., Bonavita et al. 2016; Matson et al. 2018). We also provide deep imaging of the environment of K2 targets, for which the vetting is still rare (Matson et al. 2018), and many exoplanetary candidates are not yet confirmed.

R.L. has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement n. 664931. R.L. thanks the Centre National d'Études Spatiales (CNES) for financial support through its post-doctoral program. O.D. acknowledges the support from Fundao para a Cincia e a Tecnologia (FCT) through national funds and by FEDER through COMPETE2020 by grants UID/FIS/04434/2013 & POCI-01-0145-FEDER-007672 and PTDC/FIS-AST/1526/ 2014 & POCI-01-0145-FEDER-016886. S.C.C.B. acknowledges support from FCT through national funds and by FEDER through COMPETE2020 and POCI by these grants UID/FIS/04434/2013 & POCI-01-0145-FEDER-007672 & POCI-01-0145-FEDER-028953 and through Investigador FCT contract IF/01312/2014/CP1215/CT0004. This work has made use of the SPHERE Data Centre, jointly operated by OSUG/IPAG (Grenoble), PYTHEAS/LAM/CeSAM (Marseille), OCA/Lagrange (Nice), and Observatoire de Paris/LESIA (Paris), and is supported by a grant from Labex OSUG@2020 (Investissements d'avenir—ANR10 LABX56). This work is based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programs 98.C-0779(A) and 99.C-0.276(A). This publication makes use of VOSA, developed under the Spanish Virtual Observatory project supported from the Spanish MICINN through grant AyA2008-02156. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

The TD observed in a light curve, taking into account the presence of contaminants, is given by

$$\begin{eqnarray}&&{\delta }_{\mathrm{obs}}=(1-c)\,{\delta }_{c=0},\end{eqnarray} \tag{ 1 }$$

where δ_obs is the observed TD, δ_c=0 is the TD in absence of contaminants, and c is the contamination of the light curve. c can be described as the percentage of the flux, in the photometric aperture, which comes from the contaminants (and thus not from the eclipsing system). It can be mathematically expressed as c = F_c/(F_c + F_es), where F_es is the flux coming from the eclipsing system and F_c is the flux coming from all the contaminants. Equation (1) can be transformed to obtain the difference in magnitude (Δmag) between the flux from the eclipsing system and the flux from the contaminants necessary to produce an observed depth (δ_obs), assuming an uncontaminated TD (δ_c=0):

$$\begin{eqnarray}\begin{array}{rcl}{\rm{\Delta }}\mathrm{mag} & \simeq & \mathrm{mag}({F}_{{\rm{ES}}})-\mathrm{mag}({F}_{{\rm{C}}}+{F}_{{\rm{ES}}})\\ & = & -2.5\mathrm{log}({\delta }_{\mathrm{obs}}/{\delta }_{c=0}).\end{array}\end{eqnarray} \tag{ 2 }$$

We note that the higher the δ_c=0, the higher the Δmag. Consequently, the faintest eclipsing system that can mimic a planetary transit is 10 mag fainter than the target star for an Earth-sized transit (δ_obs = 100 ppm) and 7.5 mag fainter for a Neptune-sized transit (δ_obs = 1000 ppm).

In this section, we give more details on our K2 targets, along with information on the transit detections (Table 3).

The two stars EPIC 206144956 (BD-115779) and EPIC 206011496 (BD-156276) show a V-shaped transit, typical of a grazing transit. For EPIC 206144956, a planetary candidate of 1.65 R_⊕ was detected (Vanderburg et al. 2016b). Similarly, the light curve of EPIC 206011496 reveals a transit signal corresponding to a 1.62 ± 0.12 R_⊕ exoplanet (Vanderburg et al. 2016b). Crossfield et al. (2016) used HRI with the Keck/NIRC2 instrument as complementary observations, which did not allow them to validate the exoplanetary candidate. However, they mention another companion candidate of Δmag = 2.81 in the K band at 0980 separation. This candidate was also detected in other low-resolution Keck/NIRC2 observations from 2015 August 04 (program N151N2, PI Ciardi) at 2.169 μm. The astrometry provides a separation of 979 ± 5 mas and a PA of 24827 ± 029, corresponding to Δα = −910 ± 5 mas and Δδ = −363 ± 5 mas (see Lam et al. 2018 for details).

The system of EPIC 220383386 (HD 3167) is composed of three super-Earth-sized exoplanets. The first two, HD 3167 b and HD 3167 c, were recently discovered by Vanderburg et al. (2016a) with the transit method. They performed additional imaging follow-up using Robo-AO adaptive optics system (Baranec et al. 2014; Law et al. 2014). Their images allow contrasts of 2 mag at 025 from the star, and 5 mag at 1'', and did not lead to any additional detection. However, using orbital analysis, they hypothesized that an additional non-transiting exoplanet could be part of the system. This was confirmed by RV measurements by Christiansen et al. (2017), who also gave the densities of the two transiting exoplanets. Christiansen et al. (2017) performed additional HRI vetting with the Keck/NIRC2 camera, without the detection of an additional companion.

Concerning EPIC 205904628 (HD 212657) and EPIC 206247743 (BD-096003), the TDs correspond to exoplanets of 2.13 R_⊕ and 1.67 R_⊕, respectively. Van Eylen et al. (2016) performed HRI follow-up observations of EPIC 206247743 using the FastCam camera at the Telescopio Carlos Sanchez telescope and the Subaru telescopes Infrared Camera and Spectrograph. Both observations led to no detection, but the reached contrasts did not allow us to discriminate between contaminants capable of mimicking a small planetary transit.

Finally, we have little information on EPIC 206157908 (HD 216252). The TD could correspond to an Earth-sized to Neptune-sized exoplanet, but no additional HRI follow-up observation has been performed to our knowledge.

Appendix C comprises Table 4.

Appendix D comprises Figure 5.

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